I was attempting a question and wondered how I could go about obtaining an original function from the definition of several of its compositions.
i.e.
Consider $g: \mathbb{R} \rightarrow \mathbb{R}$
$(g \circ g \circ g)(a) - a = (g \circ g)(a)\,\,\,\,\,$ $\forall a \in \mathbb{R}$
How can I obtain $g(a)$?
I tried setting $(g \circ g)(a) = h$ and substituting it in to get $g(h) = h + a$ but I want its definition to pass $a$ as the input, not specifically $(g \circ g)(a)$.
Hints but not full answers would be appreciated!